The pronunciation is roughly the following:

/tomma'?ini/

The "o" is a closed vowel, the "m" is a long consonant (typical of Italian), the two "i" are slightly longer than the "i" in "brick" and ? is...

Hey, that's the rub! In Northern Italy people would certainly pronounce it as "z" in English, this normally happens when a "s" is between two vowels.

In Southern Italy, people would certainly pronounce it like "s" in "sun".

In other words, it depends on the Italian region where a speaker is from. Unlike in English (lose vs. loose, his vs. hiss, plays vs. place), there are no minimal pairs involving the two sounds /s/ and /z/. For this reason, Italians do not really care, in all likelihood they will not even hear the difference, or vaguely sense the speaker is from another part of the country, but certainly do not confuse the meaning of a word because of this tiny detail.

In addition to this, I should like to mention this surname has a slight variation: "Tomassini". In this case, the double "s" is a long consonant and sounds like "s" in "sun" (undoubtedly). Make sure the surname is right, confusing the two is quite easy.

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Note added at 31 mins (2006-01-04 12:23:28 GMT)
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Since I read you are Russian, let me explain it some other way: áóêâà "s" ïðîèçíîñèòñÿ "ñ" èëè "ç", â çàâèñèìîñòè îò îáëàñòè. Íî â îòëè÷èè îò ðóññêîãî ÿçûêà (ñëîé è çëîé, ñìåé è çìåé...) - ýòî ñîâñåì íå âàæíî, ïðîñòî íåâîçìîæíî ïóòàòü çíà÷åíèå.

֏!